A problem with fractions.

Problem 1.

Renee used 1/3 of a length of pipe and later used 2/3 of what remained.
What fraction of the pipe is left?

Could you help me solve it?
I figured out the answer in diagram form but i am pretty sure there would be a more logical way to solve it. Please help because this is my math homework. Should be easy for some people because it was from a year nine textbook.
The answer in the back of the text book said 2/9
I need to show the working out and i would like to know how. So an explanation would be good